Re: Construct graph with virtices

a) Take a pentagon, put a 6th vertex in the middle. Connect the middle vertex to all vertices of the pentagon. Pick a vertex on the pentagon. Remove the two edges adjacent to this vertex and on the pentagon (i.e., not towards the middle vertex). Add a 7th vertex without any edges. This is your graph.

b) It is often easier to create the complementary graph. So, try creating a 2-regular graph on 6 vertices (there are 2 such graphs, up to isomorphism).